We consider the identification of a distributed parameter in an elliptic variational inequality. On the basis of an optimal control problem formulation, the application of a primal-dual penalization technique enables us to prove the existence of multipliers giving a first order characterization of the optimal solution. Concerning the parameter we consider different regularity requirements. For the numerical realization we utilize a complementarity function, which allows us to rewrite the optimality conditions as a set of equalities. Finally, numerical results obtained from a least squares type algorithm emphasize the feasibility of our approach.

Keywords: bilevel problem, complementarity function, inverse problem, optimal control, variational inequality

@article{M2AN_2001__35_1_129_0, author = {Hinterm\"uller, Michael}, title = {Inverse coefficient problems for variational inequalities : optimality conditions and numerical realization}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, publisher = {EDP-Sciences}, volume = {35}, number = {1}, year = {2001}, pages = {129-152}, zbl = {0978.65054}, mrnumber = {1811984}, language = {en}, url = {http://www.numdam.org/item/M2AN_2001__35_1_129_0} }

Hintermüller, Michael. Inverse coefficient problems for variational inequalities : optimality conditions and numerical realization. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 1, pp. 129-152. http://www.numdam.org/item/M2AN_2001__35_1_129_0/

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